Typically, a cased hydrocarbon well includes a borehole drilled in a geological formation, a fluid-filled casing disposed in the borehole and cement disposed in an annulus between the casing and the formation. During well logging operations, it can be important to obtain information as to the current condition of the casing. Ultrasonic logging tools can be used to determine the thickness of the borehole casing and the acoustic impedance of material behind the casing (e.g., cement, water, drilling mud, air, etc.). Typically, these measurements are based on exciting a casing thickness mode resonance, measuring the temporal period and amplitude decay rate, and interpreting the data. The thickness mode resonance of the casing in response to the acoustic pulse generally depends on the cement-casing bond, expressed as an acoustic impedance of the cement, and the casing thickness, which are the primary parameters of interest in the casing inspection. These parameters can be determined from a characterization of a thickness mode resonance of the casing.